Question: Solve for $a$. $0.25a+0.5 = 4.5$
Let's subtract and then divide to get $a$ by itself. $\begin{aligned} 0.25a +0.5&= 4.5 \\ \\ 0.25a+0.5 {-0.5}&= 4.5{-0.5}~~~~{\text{subtract }0.5} \text{ from each side}\\ \\ 0.25a+\cancel{ 0.5} {{-}\cancel{{0.5}}}&= 4.5{-0.5}\\ \\ 0.25a &=4.5{-0.5}\end{aligned}$ $\begin{aligned}0.25a &= 4 \\ \\ \dfrac{0.25a}{{0.25}} &= \dfrac{4}{{0.25}} ~~~~~~~\text{divide each side by } {0.25} \text{ to get } a \text{ by itself }\\ \\ \dfrac{\cancel{0.25}a}{\cancel{{0.25}}} &= \dfrac{4}{{0.25}} \\ \\ a &= \dfrac{4}{{0.25}} \end{aligned}$ The answer: $a={16}$ Let's check to make sure. $\begin{aligned} 0.25a+0.5 &= 4.5 \\\\ 0.25({16})+0.5 &\stackrel{?}{=} 4.5 \\\\ 4+0.5 &\stackrel{?}{=} 4.5 \\\\ 4.5 &= 4.5 ~~~~~~~~~~\text{Yes!} \end{aligned}$